Answer to Question #249202 in Statistics and Probability for yara

Question

A sample of 𝑛=18 observations is drawn from a normal population with 𝜇=960 and 𝜎=220. Find each of the following:

A. 𝑃(𝑋 >1037)

Probability = 

B. 𝑃(𝑋 <877)

Probability = 

C. 𝑃(𝑋>934)

Probability = 

Answer 1

A.

$z=\frac{x-\mu}{\sigma/\sqrt{n}}=\frac{1037-960}{220/\sqrt{18}}=0.08$

$P(X>1037)=1-P(z<0.08)=1-0.53188=0.46812$

B.

$z=\frac{877-960}{220/\sqrt{18}}=-0.09$

$P(X<877)=P(z<-0.09)=0.46414$

C.

$z=\frac{934-960}{220/\sqrt{18}}=-0.03$

$P(X>934)=1-P(z<-0.03)=1-0.48803=0.51197$